
Quick Reference ……………………………………….. 1

Introduction ……………………………………………. 3

KISS Principles – 10 Simple Rules ……………………. 4

What on Earth is That? ………………………………… 5

Braille Indicators ………………………………………. 6 o Number Sign o Grade 1 Indicators

Signs of ………………………………………………… 7 o Operations o Comparison o Grouping

Fractions ……………………………………………….. 8

Decimals ……………………………………………….. 9

Superscripts and Subscripts ……………………………. 9

Square Roots …………………………………………… 9

Greek Letters ………………………………………….. 10

Print Symbols …………………………………………. 10

Formatting …………………………………………….. 10

List of Common Symbols …………………………….. 11
Acknowledgements
Thanks go to the Ministry of Education for their support in the development of this resource which is licensed under the Creative
Commons Attribution-Noncommercial-Sharealike licence. To view a copy of this licence, visit http://creativecommons.org/licenses/by-ncsa/3.0/nz/
The members of the 2008 UEB Curricula Support Writing Group were
Elaine Gilmour, Jenny McFadden, Catherine West, Diane Glynan, Janet
Reynolds, Isobel Dinning and Steve Bellamy.

U E B M A T H S Q U I I C K R E F E R E N C E
Print
UEB
#a
Print
+
UEB Print
"6
#b
- "-
1
4
x

"8
"/
"
± _6
¢ @c
. "4
$ @s
: 3
% .0 = "7

° ~j square root % +
<
>
@<
@>
// fraction line
/
 _@<

#=
 _@>
angle indicator
 _[
≠ "7@:
π .p
9
Examples
32+26 = 58
#cb"6#bf "7 #eh ¾ #c/d
5¾
#e#c/d
5
2
= 25
#e9#b "7 #be
;%#d+
-3
"-#c
UEB
"<
">
$#c
$#d
$=
\
\o
#l
#-
+
_
Revised October 2013
1

2
Revised October 2013

3
Introduction
The Hitchhiker’s Guide to UEB first edition was written in 2008 by a group of dedicated
Resource Teachers Vision from the Blind and Low Vision Network New Zealand together with support from staff at the Royal New Zealand Foundation of the Blind, Accessible Format
Production.
The team members gifted their time, knowledge and passion for braille, to produce a resource to support staff, learners and producers with Unified English Braille (UEB) production, as New
Zealand’s adoption of UEB became a reality in the education and braille worlds.
The Hitchhiker’s Guide to UEB was developed to serve as a quick memory jogger. It is not a comprehensive braille instruction guide. This edition, updated in 2013, reinforces the use of the guide as a reference tool to be used by Resource Teachers Vision (RTVs), teachers, teacher aides, Whānau and parents, who find themselves needing to braille texts quickly for student use.
For more in-depth braille rules please refer to the Braille Authority of New Zealand Aotearoa
Trust BANZAT website at www.banzat.org.nz
from which the current editions of the manuals listed below can be downloaded.

Unified English Braille Manual: New Zealand Edition

Unified English Braille Guidelines for Technical Material

The Rules of Unified English Braille
Revised October 2013

(Keeping it so simple!)
1.
+ - x ÷ = all take dot 5
2.
money symbols take dot 4 and are followed by number sign
3.
operation signs are unspaced both sides
4.
comparison signs are spaced before and after
5.
greater than and less than signs take dot 4
6.
simple fraction line –
/
7.
mixed numerals – repeat number sign
8.
superscript – change level up ( 9 )
9.
subscript – change level down ( 5 )
10.
square root has to open and close ( % … + )
Revised October 2013
4

5
Dot 4 symbols
@s
@c
@e
@a
$
¢
€
@
Dots 4, 5 symbols
~j
~9 
°
_6
Dots 4, 5, 6 symbols
plus or minus
_@>
_@<
≥
≤ greater than or equal to
less than or equal to
.0
./
%
Dots 4, 6
general fraction line
Dot 5
"6
+ plus
"-
– minus
"8
× multiply
"4
multiplication
dot
@<
@ >
<
>
@.< open
transcriber’s note
@.> close
transcriber’s note
_/
_9
(tilde over horizontal line)
_[ ∠
/ approximately equal to
.p π
.a
α
.b
β
,.s Σ capital Sigma
"/ ÷ divide
"7
= equals
"7@: ≠
not equal to
.<
[ square brackets
.>
]
"9
* asterisk
@: line through
previous item
(cancellation, "not")
",-
____ long dash, typically used to indicate missing answer e.g.
"7@: ≠
Dot 5 is used as the numeric space symbol to indicate when a space has been used instead of a comma e.g. 1 000 000
#a"jjj"jjj
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6
In UEB each print symbol has one and only one braille equivalent.
UEB Maths is not a separate code. All the symbols you would meet in UEB literary material are the same when met in a maths setting.
Braille Indicators
The limitations of the 6-dot cell make it impossible to represent in braille, without duplication, the many arbitrary signs used in print mathematics. A system of braille indicators is therefore used. These indicators have no corresponding ink print signs but impart particular meanings to the braille symbols which precede or follow them.
Number Sign (dots 3 4 5 6)
The most common braille indicator is the number sign which signals that the following cell (or cells) forms a number. The digits one to nine and zero are shown by the letters a to j preceded by the number sign. e.g. 1
#a
500
#ejj
Grade 1 Indicators (dots 5 6)
If a braille symbol also has a Grade 2 meaning then the Grade 1 Indicator must be used unless Grade 1 mode is already in force.
; indicates the following symbol is in Grade 1
;;
;;;
;'
(dots 56, 3) terminates the Grade 1 passage.
Any algebra expression may need a Grade 1 Word Indicator or, if it includes spaces, a Grade 1 Passage Indicator . A simple arithmetic equation will not.
The Number Sign acts as a Grade 1 indicator.
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7
Signs of Operation
The basic mathematical operations are addition, subtraction, multiplication and division. These are 2-cell signs. plus +
"6
(dot 5, dots 2 3 5) minus -
"-
(dot 5, dots 3 6) multiply ×
"8
(dot 5, dots 2 3 6) divide ÷
"/
(dot 5, dots 3 4) plus or minus ±
_6
(dots 4 5 6, dots 2 3 5) multiplication dot .
"4
(dot 5, dots 2 5 6)
The signs of operation are unspaced. e.g 6+3, 4-2, 8×9
#f"6#c1 #d"-#b1 #h"8#i
Signs of Comparison
In braille these are at least 2-cell signs and must be preceded and followed by a space.
The most common is the equals sign. Others include the symbols for greater than >, less than <, etc. equals = greater than > less than <
"7
(dot 5, dots 2 3 5 6)
@>
(dot 4, dots 3 4 5)
@<
(dot 4, dots 1 2 6) not equal to
  "7@:
(dot 5, dots 2 3 5 6, dot 4, dots 1 5 6) e.g. 6+3 = 9
#f"6#c "7 #i
Signs of Grouping
The basic brackets are
Round brackets ( )
"< ">
(opening: dot 5, dots 1 2 6; closing: dot 5, dots 3 4 5)
Square brackets [ ]
.< .>
(opening: dots 4 6, dots 1 2 6; closing: dots 4 6, dots 3 4 5)
Curly brackets { }
_< _>
(opening: dots 4 5 6, dots 1 2 6; closing: dots 4 5 6, dots 3 4 5)
Revised October 2013

8
Braille Enclosure Indicators
Braille grouping indicators are used when there are no print brackets but the symbols still need treating as an item. See the last examples in the Superscripts and Subscripts
Section on the next page. opening
<
(dots 1 2 6) closing
>
(dots 3 4 5)
Simple Fractions
In braille, fractions are a little different from the print forms because they are written across the line. We do not talk about the top and bottom parts of a fraction; we refer to them by their correct names – numerator and denominator.
In print, simple fractions may be written either as 3 or as 3/4 and in both cases we
4 would say either “three quarters” or “three over four”. Be consistent and use the same form for each case.
3
#c/d
5½
#e#a/b
4
Complex Fractions
When you have fractions with more complex numerators or denominators you will need to indicate that it is a fraction by using the General Fraction Open and Close
Indicators.
Opening
(
(dots 1 2 3 5 6) closing
)
(dots 2 3 4 5 6)
Since the General Fraction Open Indicator has a Grade 2 meaning the following examples use a Grade 1 Indicator .
3+6
;(#c"6#f./#d)
4
x
;(x./#b)
2
Revised October 2013

Decimal Point
The symbol used for the decimal point is dots 2 5 6
4 – the same as the full stop because a decimal point looks like a full stop.
Superscripts and Subscripts (Level Indicators)
Superscripts have changed level up and are indicated by
9
3
2 #c9#b
If letters are involved then the level indicator could be a contraction so a Grade 1 indicator is needed. y
2 y;9#b
A level indicator only refers to the next item. If a superscript contains more than one symbol – e.g. y
-2
, x
4+5
the items -2 and 4+5 must be enclosed in braille grouping symbols.
y
-2 ;;y9<"-#b> x
4+5 ;;x9<#d"6#e>
Notice that the Grade 1 word indicator covers all the possible contractions in this expression.
Subscripts have changed level down. They are indicated by
5
and the rules are the same.
Square Roots and other Radicals
The expression inside the square root sign in print (the radicand) should be preceded by the open radical sign and followed by the close radical sign. opening
%
(dots 1 4 6) closing
+
(dots 3 4 6)
4
;%#d+
Both the opening and closing radical signs have alternative grade 2 meanings so we need the Grade 1 Indicator.
9
Revised October 2013

10
Greek Letters
Greek letters are used quite a lot in maths, for various reasons. The most famous is, of course, pi – or as the Greeks write it,
π.
The Greek letters usually correspond to print letters e.g. alpha is “a”, but some have no single letter equivalent e.g.
θ
theta.
The symbol used to indicate that the next letter is a Greek letter is dots 4 6. e.g.
α
(alpha)
.a
β
(beta)
.b
θ
(theta)
.
?
π
(pi)
.p
σ
(sigma)
.s
Σ
(sigma – upper case)
,.s
Note that the capital sign comes before the Greek letter symbol.
Print Symbols
If the print character looks like a letter of some kind then the braille often uses that letter, preceded by the prefix dot 4. e.g. $
@s
(dot 4, s)
@
@a
(dot 4, a)
See the UEB Symbols list, or Guidelines for Technical Materials, for a full set of
Maths symbols.
Formatting
The normal braille line has space for 40 cells. Make sure the brailler is set at this length.
Begin at the very first cell of the line. If the equation or the problem has to extend on to subsequent lines these are called “run-overs”. Run-overs go in cell 3 of the second and following lines.
In 2- or 3-step equations which overrun make sure that the equals sign stays with the answer. Normally this means that the run-over line would start with the equals sign.
This makes it easy for the student to review and for the teacher to mark.
Revised October 2013

11
Date
Print
28-5-2014 #bh-#e-#bjad
19/1/2014 #ai_/#a_/#bjad
UEB
Numbers, money, measurement
Print UEB Name Examples
1 #a digit one
1
5 st th
#ast first
#eth fifth
. 4
12 0 300
#ab #j #cjj
#ast
#eth decimal point
0.56 (decimal)
#j4ef
.7
#4g
, 1
" comma
¢ @c cent
1,000,000
#a1jjj1jjj numeric space 1 000 000 #a"jjj"jjj
99¢
#ii@c
$ @s dollar
% .0 percent
° ~j degree
$44.99
@s#dd4ii
50% of $2.50
#ej.0 ( @s#b4ej
3 ° C
#c~j ;,c cm m km g kg mL
L cm
;m
Km
;g kg
M,l
;,l centimetre metre kilometre gram kilogram millilitre litre
0.45 cm
#j4de cm
0.45 m
#j4de ;m
45 km
#de km
500 g
#ejj ;g
5 kg
#e km
250 mL
#bej M,l
5 L
#e ;,L
Revised October 2013

12
Operation signs
Print UEB Name Example
+ "6 plus
- "- minus x "8 multiplied by
9+3
#i"6#c
7-2
#g"-#b
12 x 12
#ab"8#ab
. "4 multiplication dot 3.a #c"4a
 "/ divided by
39

13
#ci"/#ac
: 3 ratio
± _6 plus or minus
3 : 4
#c3#d x
±
3
x_6#c
% + square root
!
6 factorial sign
4
;%#d+
N.B. the square root symbols enclose the number
6!
#f6
Comparison signs
Print UEB Name Example
= "7 Equals
> @> greater than
4+5 = 9
6>5
#d"6#e "7 #i
#f @> #e
< @< less than
4<5
#d @< #e
 _@> greater than or equal to
4

d
#d _@> ;d
 _@< less than or equal to
6
 x #f _@< ;x
≠ "7@: not equal to 4 ≠ 8 #d "7@: #h
Time
Print UEB Example
5:30 pm
5.30 am
1300 hrs
80 km/h
#e3#cj pm
#e4cj am
#acjj hrs
#hj Km_/h
Revised October 2013

13
Fractions
Print UEB Name
/ / simple numeric fraction line
./
general fraction line
( general fraction open indicator
) general fraction close indicator
Example
3
4 or
3
4
#c/d
5 ½
#e#a/b a+6
;(a"6#f./#d)
4
NB Number sign must be repeated after the general fraction line.
Superscripts and Subscripts
UEB Name Example
9 superscript – change level up. 3
2 #c9#b y
2 y;9#b y
-2 ;;y9<"-#b> x
4+5 ;;x9<#d"6#e>
5 subscript – change level down.
P
1
,P;5#a
100
2
#ajj5#b
Miscellaneous mathematical symbols
Print UEB Name
∞ #= Infinity
 _[ angle sign
// #l parallel to
 #- perpendicular to
 ,* therefore
∵ @/
+ since general omission symbol
Shapes
Print UEB Name
$ shape indicator
$#c regular (equilateral) triangle
$#d square
$#e regular pentagon (5-sided figure)
$= circle
Revised October 2013

14
Arrows
UEB Name
\ arrow indicator
\o simple right pointing arrow (east) →
\[ simple left pointing arrow (west)
←
\+ simple up pointing arrow (north)
↑
\% simple down pointing arrow (south)
↓
And just because …
Bullets, Barbs and Daggers!
UEB
 _4
↠ r
;\33rro
† @,?
Name bullet regular barb, full, in line of direction double-barbed arrow dagger
Revised October 2013